# Is there work done on a mass from matter-antimatter pairs?

Imagine I have a vaccuum at very low temperature and I put a single neutron in, then gamma rays interact to form matter-antimatter pairs within this vaccuum and assume that this happens extremely close to the aforementioned neutron. Since the matter-antimatter pair has mass, there would be a small amount of curvature in spacetime. Would the neutron follow the geodesic created? If so, this means that there was work applied onto the neutron from no initial force. Which would mean a violation in the conservation of energy/force. What is the flaw in this situation?

If the mass of the neutron >>> mass of electron/positron is the issue, then replace the neutron with an electron. Here there would also be either an attractive or repelling electromagnetic force depending on orientation, which still leads to my point.

I am still in high school, so I have a very limited understanding of these topics, sorry for my naivety. But so far the teachers I have asked have not given me a satisfactory response yet.

• Why do you claim there is a violation of conservation of energy ??(conservation of force is not a thing I know of) First of all, the gamma ray itself will curve spacetime because it is energy, not mass only, that generates a curvature. So the "free" energy that made your neutron move is not free at all, it was provided by the energy of the gamma ray you sent in. Tell me if I am misunderstanding something – Frotaur Mar 10 '20 at 13:57

## 1 Answer

It is not possible to have the topology you describe. In order for a gamma ray to create a particle antiparticle pair, it needs the electromagnetic field of a nucleus for energy and momentum conservation to work in the center of mass of the e+e- pair. In this feynman diagram Z is the nucleus in whose electromagnetic field the pair production can happen.

So you cannot have a neutron and a particle pair only.

As for gravitational interactions, yes, as long as there is an energy momentum tensor the solutions of the General Relativity are followed by all particles . Zero mass particles follow the geodisics, massive ones the solutions of the particular boundary condition problem.